Several examples with detailed solutions and exercises with answers on addition of fractions, are presented.

is used here to denote the fraction of a over b. a is called the numerator and b is called the denominator and must be non zero.

Examples of fractions:

NOTE: is undefined since division by zero is undefined in mathematics.

A calculator to add fractions is included in this website. You may use it to check your answers.

## 1. Add fractions with equal denominator

Solution to Example 1

To add fractions with the same denominator, you add the numerators, keep the same denominator and simplify if possible

Example 2: Add, simplify and express the final answer as a fraction.

Solution to Example 2

## 2. Add fractions with non equal denominators

Example 3: Add, simplify and express the final answer as a fraction.

Solution to Example 3

We first need to find the lowest common multiple (LCM) of the denominators 9 and 6 by factoring into prime factors.

We next convert the two given fractions so that they have common denominator equal to the LCM = 18. The denominator of the fraction is 9 and we need to multiply numerator and denominator by 2 in order to change the denominator to 18

The denominator of the fraction is 6 and we need to multiply numerator and denominator by 3 in order to change the denominator to 18

Now that we have converted the two fractions so that they have common denominator, we can easily add them as follows

Example 4: Add, simplify and express the final answer as a fraction and as a mixed number.

Solution to Example 4

Find the LCM of the denominators 15 and 55

We convert the given fractions so the they have common denominator equal to the LCM = 165. The denominator of the fraction is 15 and both numerator and denominator need to be multiplied by 11 in order to change the denominator to 165

The second fraction is converted to one with the denominator equal to 165 by multiplying numerator and denominator by 3 in order to change the denominator to 165

Example 5: Add, simplify and express the final answer as a fraction.

Solution to Example 5

We first convert 2 into a fraction

The common denominator will be 5